All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Pier Operator (Posted on 2008-12-13)
Substitute each of the letters by a different decimal digit from 0 to 9 to satisfy this alphametic square root extraction problem. None of O and P can be 0.

P I E R
--------------------
√ O P E R A T O R |
C T
------------
B E R
B A C
------------------
E  P A T
T  I A  I
----------------------
P I  E O R
P I  E O R
----------------------

Note: Try to derive a non computer assisted method, although computer program/spreadsheet solutions are welcome.

 See The Solution Submitted by K Sengupta No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 Without knowing the whole square-root algorithm (computer assisted soln) | Comment 1 of 2
A computer program that considers only whether PIER^2 = OPERATOR yields:

```4975          24750625
5061          25613721```

but the second one is ruled out as P*P would be OP, rather than the different CT shown.

OPERATOR is therefore 24750625, while
PIER is 4975.

And C is 1 and B is 24-16 = 8.

Thus, one need not know the entire square-root algorithm.

DEFDBL A-Z
FOR p = 1 TO 9
FOR o = 1 TO 9
FOR i = 0 TO 9
FOR e = 1 TO 9
FOR r = 0 TO 9
FOR a = 0 TO 9
FOR t = 1 TO 9

pier = p * 1000 + i * 100 + e * 10 + r
operator = o * 10000010 + p * 1000000 + e * 100000 + r * 10001 + a * 1000 + t * 100
IF pier * pier = operator THEN PRINT pier, operator

END IF
NEXT
END IF
NEXT
END IF
NEXT
END IF
NEXT
END IF
NEXT
END IF
NEXT
END IF
NEXT

Note the program considers that E and T are also non-zero in keeping with the spirit of such things, though the same two possibilities are supplied even if zero is allowed for these two variables.

 Posted by Charlie on 2008-12-13 19:24:34

 Search: Search body:
Forums (0)